Juan C. Moreno

Department of Mathematics

University of Notre Dame

Office: Hurley 260

Email: jmoreno9@nd.edu

Pronouns: he/him

About Me

I am a postdoc at the University of Notre Dame working with Mark Behrens.

I completed my PhD in Spring 2025 at the University of Colorado Boulder, advised by Agnès Beaudry.

Before that, I was at the University of Texas at Austin, where I received a Bachelor of science in math and physics.

My research interests lie generally in the areas of stable homotopy theory, and interactions between algebraic topology and physics.

You can find my CV here (last updated Nov. 2024).

Research

Ongoing

The Real v_n-Bockstein spectral sequence.

The pictures at the top and bottom of this page illustrate a Bockstein spectral sequence computing the homotopy groups of tmf_0(3) from the RO(C_2)-graded homotopy groups of Atiyah Real K-theory. I'm currently thinking about generalizations of this computation to truncated norms of Real bordism.

Real homological trace methods.

With Myungsin Cho, Teena Gerhardt, Liam Keenan, and J.D. Quigley. We are working towards constructing suitable parametrized versions of the homological S^1-homotopy fixed point and S^1-Tate fixed point spectral sequences with the hope to apply them to the Real topological Hochschild homology of truncated Real Brown-Peterson spectra.

Preprints

Publications

Duals of higher real K-theories at p=2. ArXiv version.

Advances in Mathematics (2026). Published version.

Homotopical Foundations of Parametrized Quantum Spin Systems. ArXiv version.

With A. Beaudry, M. Hermele, M. Pflaum, M. Qi, and D. Spiegel.

Reviews in Mathematical Physics (2024). Published version.

Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems. ArXiv version.

With X. Wen, D. Spiegel, A. Beaudry, M. Qi, M. Hermele, A. Vishwanath, and M. Pflaum.

Phys. Rev. B. Volume 108, Issue 12. American Physical Society (2022). Published version.

Continuous Dependence on the Initial Data in the Kadison Transitivity Theorem and GNS Construction. ArXiv version.

With D. Spiegel, M. Qi, M. Hermele, A. Beaudry, and M. Pflaum.

Reviews in Mathematical Physics (2022). Published version.

Teaching

University of Notre Dame

Spring 2026 Instructor MATH 20580 Intro to linear algebra & differential equations.
Fall 2025 Instructor MATH 10350 Calculus A

University of Colorado Boulder

Spring 2025 Instructor MATH 2300 Calculus 2
Spring 2024 TA MATH 2300 Calculus 2
Spring 2023 TA MATH 2300/2400 Calculus 2/3
Fall 2022 Instructor MATH 2400 Calculus 3
Fall 2021 Instructor MATH 2300 Calculus 2
Spring 2021 TA MATH 2400 Calculus 3
Spring 2020 TA MATH 2300 Calculus 2
Fall 2019 TA MATH 1300 Calculus 1

University of Texas at Austin

Spring 2018 LA M408S Integral Calculus for Science
Fall 2017 LA M408L Integral Calculus